Newsgroups: alt.fractals
Path: unixg.ubc.ca!ubc-cs!van-bc!zaphod.mps.ohio-state.edu!rpi!usenet.coe.montana.edu!milton!jesjones
From: jesjones@milton.u.washington.edu (Jesse Jones)
Subject: Re: Better Mandelbrots and Julians
Message-ID: <1992Jan14.234002.16985@milton.u.washington.edu>
Summary: My favorite formula
Organization: University of Washington, Seattle
References: <1582@lhdsy1.chevron.com> <1992Jan10.225034.256@nntp.uoregon.edu> <13JAN199214533040@reg.triumf.ca>
Date: Tue, 14 Jan 1992 23:40:02 GMT
 
The best formula I've ever seen is a Newton variant. The images look similar to
the typical Newton fractals but there are distorted copies of the M-set
scattered about. Some of the distorted mandelbrots are very strange. But the
best thing about this fractal is the way it looks when decomposition is used.
The results are stunning.
 
The formula is z := z - p(z)/[p'(z) + ki) where p(z) = (z-1)*(z^2+z+.25-c^2).
z is inited to zero and c is inited to a point on the complex plane. k is any
real number (I usually use zero). As is usual for Newtons the bailout condition
is that p(z) is near zero.
 
  --Jesse